document.write( "Question 1054915: y/4+z/4=z/3+x/3=x/2+y/2
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Algebra.Com's Answer #670150 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "You are given these THREE equations\r\n" );
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document.write( "y/4+z/4 = z/3+x/3,   (1)\r\n" );
document.write( "z/3+x/3 = x/2+y/2,   (2)\r\n" );
document.write( "x   + y  + z = 27.   (3)\r\n" );
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document.write( "Multiply (1) by 12 (both sides) and (2) by 6 (both sides). You will get\r\n" );
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document.write( "3y + 3z = 4z + 4x,   (1')\r\n" );
document.write( "2z + 2x = 3x + 3y,   (2')\r\n" );
document.write( "x +   y +  z = 27    (3')\r\n" );
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document.write( "Or, which is the same (simplifying)\r\n" );
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document.write( "4x - 3y +  z = 0,    (1'')\r\n" );
document.write( "x  + 3y - 2z = 0,    (2'')\r\n" );
document.write( "x  +  y +  z = 27.   (3'')\r\n" );
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document.write( "Add (1'') and (2'') (both sides). You will get\r\n" );
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document.write( "5x - z = 0,   or   z = 5x.\r\n" );
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document.write( "Now substitute z = 5x into (1'') and (3''). You will get\r\n" );
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document.write( "4x - 3y + 5x =  0,    (4)  instead of (1'') and\r\n" );
document.write( "x  +  y + 5x = 27     (5)  instead of (3'').\r\n" );
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document.write( "Simplify:\r\n" );
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document.write( "9x - 3y =  0,         (4')\r\n" );
document.write( "6x +  y = 27,         (5')\r\n" );
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document.write( "or\r\n" );
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document.write( "3x - y =  0,          (4'')\r\n" );
document.write( "6x + y = 27.          (5'')\r\n" );
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document.write( "Add (4'') and (5''). You will get\r\n" );
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document.write( "9x = 27  --->  x =  = 3.\r\n" );
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document.write( "Then from (4'')  y = 3x = 3*3 = 9.\r\n" );
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document.write( "Finally,  z = 5x = 5*3 = 15.\r\n" );
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document.write( "Answer.  x = 3,  y = 9,  z = 15.\r\n" );
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